Vertical angles are equal, so we can set the measures of the two angles equal to each other:
\[ m∠2 = m∠4 \]
Given \( m∠2 = 135° \) and \( m∠4 = (4x + 15)° \), we can set up the equation:
\[ 135 = 4x + 15 \]
Next, we can solve for \( x \):
- Subtract 15 from both sides:
\[ 135 - 15 = 4x \]
\[ 120 = 4x \]
- Divide both sides by 4:
\[ x = \frac{120}{4} = 30 \]
Thus, the value of \( x \) is \( \boxed{30} \).